MANY AMERICANS would be dumbfounded to know that a sweeping reform of the nation’s broken immigration system, passed by the Senate and backed by the White House, has virtually no chance of becoming law — even though it is probably also supported by a majority of the House of Representatives. Thanks to the opposition of House Republican conservatives, to whom Speaker John Boehner (R-Ohio) owes his power, the Senate bill will be blocked from reaching the House floor for a vote.

Hence the will of the pro-reform majority, not just of Congress but of the nation, is thwarted for now by Republicans whose congressional districts allow them to ignore the realities of a multicultural America and 11 million illegal immigrants — at least until the next presidential election.

Still there remains a chance that sanity will eventually prevail in the House, in the form of a compromise that would allow the undocumented to emerge from the shadows. To reach such a compromise, which is overwhelmingly in the nation’s economic self-interest, respected pro-reform Republicans like Rep. Paul D. Ryan (R-Wis.) must decide to push from the inside.

Mr. Boehner, in his way, has left the door open for a compromise, making it clear that the House must act and allowing for the possibility that a path to legalization could be part of the deal — if his caucus drifts in that direction. Unfortunately, he seems to regard his role in coming to such a deal as that of an event organizer rather than as a leader intent of problem-solving and governing.

Republicans in the House Judiciary Committee, meanwhile, have passed a series of piecemeal immigration bills — to tighten border security; encourage deportation and state harassment of illegal immigrants; forge ahead with employment verification; recruit (and exploit) temporary agricultural workers; and expand the number of visas for science, technology, engineering and math workers — none of which has a prayer of becoming law on its own. As has been the case for years, the political reality is that, to advance the immigration measures they want, all sides will have to swallow ones they dislike.

For Republicans, that means a pathway to legalization at the least, if not citizenship. It shouldn’t be an impossible sell. There is no doubt that granting legal status to millions of undocumented workers would help expand and energize the economy, as the Congressional Budget Office has recently affirmed. Key parts of the GOP base, including business and evangelicals, have rallied behind comprehensive reform. In the Senate, Democrats have already yielded to GOP demands that Congress double down on border security.

What more does the GOP want? A guarantee that if and when they become citizens, 13 or 15 years from now, millions of currently undocumented Hispanics will vote Republican? If their obstructionism continues, House Republicans could instead ensure something very different — that the party’s falling-out with the existing Hispanic electorate will become irreconcilable.